95% CI

Definition

A 95% confidence interval (CI) is a statistical range that is likely to contain the true population parameter 95% of the time. It provides a measure of uncertainty around a sample estimate, indicating that if we were to take many samples and compute a CI for each, approximately 95% of those intervals would capture the actual parameter. This term connects to the interpretation of results, the importance of sample size, and how variability affects estimates.

5 Must Know Facts For Your Next Test

1. A 95% confidence interval is commonly used in research to indicate reliability; it implies that there is a 5% chance the true parameter lies outside this interval.
2. The width of a 95% CI depends on the variability of the data and the sample size; larger samples tend to yield narrower intervals.
3. Confidence intervals can be calculated for means, proportions, differences between groups, and more, making them versatile in reporting statistical findings.
4. Interpreting a 95% CI does not mean there's a 95% probability that any given interval contains the parameter; rather, it's about the long-run performance of the method.
5. If a confidence interval does not include a null value (like zero for differences), it suggests statistical significance at the 0.05 level.

Review Questions

• How does the width of a 95% confidence interval relate to sample size and variability?
  • The width of a 95% confidence interval is influenced by both sample size and variability in the data. Larger sample sizes generally result in narrower confidence intervals because they provide more information about the population, reducing uncertainty. Conversely, greater variability in the data leads to wider intervals since it reflects increased uncertainty regarding where the true population parameter lies.
• Why is it important to consider confidence intervals when interpreting statistical results?
  • Confidence intervals are crucial when interpreting statistical results because they provide context around point estimates, indicating the level of uncertainty associated with them. A narrow confidence interval suggests high precision, while a wide one indicates more variability and less certainty about where the true parameter lies. By considering these intervals, researchers can make informed decisions about the reliability and significance of their findings.
• Evaluate how different sample sizes impact conclusions drawn from confidence intervals in research studies.
  • Different sample sizes significantly impact conclusions drawn from confidence intervals as they directly affect both precision and reliability. Larger samples tend to produce narrower confidence intervals, allowing researchers to make more confident claims about population parameters. On the other hand, small samples may lead to wide intervals that overlap with null values, potentially obscuring significant findings. Evaluating these impacts helps researchers assess whether their conclusions can be trusted or if further investigation with larger samples is needed.

Related terms

Margin of Error: The margin of error is the range within which the true population parameter is expected to fall, based on the sample estimate and its variability.

Point Estimate: A point estimate is a single value estimate of a population parameter derived from sample data.

Statistical Significance: Statistical significance indicates whether the results observed in data are likely due to chance or represent a true effect within the population.